Peter Baxendale

Tenure Track Appointments

• Professor of Mathematics, University of Southern California, 08/01/1988 –
• Associate Professor of Mathematics, University of Florida, 08/01/1987 – 08/01/1988
• Lecturer in Mathematics, University of Aberdeen, Scotland, 09/01/1973 – 09/01/1987

Research, Teaching, Practice, and Clinical Appointments

• Lecturer in Mathematics, University of Warwick, England, 1972-01-01-1973-01-01

Summary Statement of Research Interests

Professor Baxendale studies diffusion processes, stochastic differential equations, stochastic flows of diffeomorphisms, stability and equilibrium behavior for random dynamical systems and stochastic bifurcation theory.

His work also focuses on stability, statistical equilibrium and bifurcation theory for stochastic differential equations.

Book Chapters

• Baxendale, P. H. (1999). Stability along trajectories at a stochastic bifurcation point. pp. p. 1-25.. Stochastic Dynamics/Springer.

Journal Article

• Arratia, R., Baxendale, P. H. (2014). Bounded size bias coupling: a gamma function bound, and universal Dickman-function behavior. Probability Theory and Related Fields. (10.1007/s00440-014-0572-x), pp. 17.
• Baxendale, P. H. (2011). T.E. Harris’s contributions to recurrent Markov processes and stochastic flows. Annals of Probability. Vol. 39 (2), pp. 417-428.
• Baxendale, P. H., Greenwood, P. E. (2010). Sustained oscillations for density dependent Markov processes. Journal of Mathematical Biology. Vol. 63, pp. 433-457.
• Baxendale, P. H., Mayberry, J. (2009). A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators. Stochastic Processes and Applications.
• Baxendale, P. H., Dimitroff, G. (2009). Uniform shrinking and expansion under isotropic Brownian flows. Journal of Theoretical Probability. Vol. 22, pp. 620-–639..
• Baxendale, P. H., Picas, M. (2007). Almost sure and moment Lyapunov exponents for a stochastic beam equation. Journal of Functional Analysis. Vol. 243, pp. 566-610.
• Baxendale, P. H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Annals of Applied Probability. Vol. vol 15 (2005), pp. pp 700-738.
• Baxendale, P. H. (2004). Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation. Stochastic Processes and Their Applications/Elsevier. Vol. vol 113 (2004), pp. pp 235-272.
• Baxendale, P. H., Liptser, R., Chigansky, P. (2004). Asymptotic stability of the Wonham filter: ergodic and non-ergodic signals. SIAM Journal on Control and Optimization/SIAM. Vol. vol 43, pp. pp. 643-669..
• Baxendale, P. H., Goukasian, L. (2002). Lyapunov exponents for small random perturbations of Hamiltonian systems. Annals of Probability. Vol. vol 30, pp. pp. 101-134..
• Baxendale, P. H. (1994). A stochastic Hopf bifurcation. Probability Theory and Related Fields/Springer. Vol. vol 99, pp. pp. 581-616..

Proceedings

• Baxendale, P. H. (2005). Random sources and sinks for stochastic dynamical systems. Proceedings of ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference/Eindhoven University of Technology, The Netherlands.
• Baxendale, P. H. (2003). Lyapunov exponents and stability for the stochastic Duffing-van der Pol oscillator. pp. p. 125-135. IUTAM Symposium on Nonlinear Stochastic Dynamics (N. Sri Namachchivaya and Y.K. Lin, eds)/Kluwer Academic Publications (Kluwer).
• Baxendale, P. H. (1991). Invariant measures for nonlinear stochastic differential equations. pp. pp. 123-140. Lyapunov Exponents. Proc. Oberwolfach 1990 (L. Arnold, H. Crauel and J.-P. Eckmann eds)/Springer.

• Fellow (or Equivalent) of National Society in Discipline, Fellow of Institute of Mathematical Statistics, 1993
• Rollo Davidson Prize, University of Cambridge, 1987

Editorships and Editorial Boards

• Member of the editorial board, Stochastics and Dynamics, 2001 – 2008

Professional Memberships

• Institute of Mathematical Statistics, 1989 –
• American Mathematical Society, 1987 –
• London Mathematical Society, 1972 –